Some results on almost paracontact paracomplex Riemannian manifolds

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Atıf İçin Kopyala

Özdemir N., Aktay Ş., SOLGUN M.

AIMS Mathematics, cilt.10, sa.5, ss.10764-10786, 2025 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 10 Sayı: 5
• Basım Tarihi: 2025
• Doi Numarası: 10.3934/math.2025489
• Dergi Adı: AIMS Mathematics
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
• Sayfa Sayıları: ss.10764-10786
• Anahtar Kelimeler: almost paracontact paracomplex Riemannian manifold, Einstein manifold, Riemannian almost product manifold, warped product
• Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

In this study, a class of Riemannian almost product manifolds is obtained by the warped product of almost paracontact paracomplex Riemannian manifolds with R. The curvature properties of the almost product manifolds are studied. Then, normal almost paracontact paracomplex Riemannian manifolds are considered. It is proven that the almost paracontact paracomplex Riemannian manifolds are normal if and only if the almost product manifolds obtained by the warped product are integrable. In addition, examples of almost paracont paracomplex Riemannian manifolds are given. product structure. Thus, the product manifold is a Riemannian almost product manifold of a special type. We write the covariant derivative of the Riemannian metric and the almost product structure of product manifold in terms of the covariant derivative of the metric of the almost paracontact paracomplex Riemannian manifold. We investigate the curvature properties of the product manifold and state relations between some classes of almost paracontact paracomplex Riemannian manifolds and Riemannian almost product manifolds. In addition, the almost product manifold obtained by the warped product is integrable if and only if the almost paracontact paracomplex Riemannian manifold is normal.